Question: Solve for $x$ and $y$ using elimination. ${4x+3y = 24}$ ${-x+2y = 5}$
We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Multiply the bottom equation by $4$ ${4x+3y = 24}$ $-4x+8y = 20$ Add the top and bottom equations together. $11y = 44$ $\dfrac{11y}{{11}} = \dfrac{44}{{11}}$ ${y = 4}$ Now that you know ${y = 4}$ , plug it back into $\thinspace {4x+3y = 24}\thinspace$ to find $x$ ${4x + 3}{(4)}{= 24}$ $4x+12 = 24$ $4x+12{-12} = 24{-12}$ $4x = 12$ $\dfrac{4x}{{4}} = \dfrac{12}{{4}}$ ${x = 3}$ You can also plug ${y = 4}$ into $\thinspace {-x+2y = 5}\thinspace$ and get the same answer for $x$ : ${-x + 2}{(4)}{= 5}$ ${x = 3}$